scholarly journals Mathematical Indispensability and Arguments from Design

Philosophia ◽  
2021 ◽  
Author(s):  
Silvia Jonas
Keyword(s):  
Physical World ◽  
Natural Sciences ◽  
Empirical Testing ◽  
Mathematical Realism ◽  
Existence Of God ◽  
Natural Explanation ◽  
Applicability Of Mathematics

AbstractThe recognition of striking regularities in the physical world plays a major role in the justification of hypotheses and the development of new theories both in the natural sciences and in philosophy. However, while scientists consider only strictly natural hypotheses as explanations for such regularities, philosophers also explore meta-natural hypotheses. One example is mathematical realism, which proposes the existence of abstract mathematical entities as an explanation for the applicability of mathematics in the sciences. Another example is theism, which offers the existence of a supernatural being as an explanation for the design-like appearance of the physical cosmos. Although all meta-natural hypotheses defy empirical testing, there is a strong intuition that some of them are more warranted than others. The goal of this paper is to sharpen this intuition into a clear criterion for the (in)admissibility of meta-natural explanations for empirical facts. Drawing on recent debates about the indispensability of mathematics and teleological arguments for the existence of God, I argue that a meta-natural explanation is admissible just in case the explanation refers to an entity that, though not itself causally efficacious, guarantees the instantiation of a causally efficacious entity that is an actual cause of the regularity.

Morality and The Three-fold Existence of God

2012 ◽  
Vol 17 (1) ◽  
pp. 27-47
Author(s):  
Leslie Armour
Keyword(s):  
Practical Reason ◽  
Moral Theology ◽  
Physical World ◽  
Existence Of God

Arguments about the existence of a being who is infinite and perfect involve claims about a being who must appear in all the orders and dimensions of reality. Anything else implies finitude. Ideas about goodness seem inseparable from arguments about the existence of God and Kant's claim that such arguments ultimately belong to moral theology seems plausible. The claim that we can rely on the postulates of pure practical reason is stronger than many suppose. But one must show that a being who is infinite and perfect is even possible, and any such being must be present in the physical world as well as in what Pascal called the orders of the intellect and morality (which he called the order of charity). Indeed, locating God in the various orders without creating conflicts is problematic. Such arguments are necessarily difficult and sometimes self-defeating but I argue in this paper that there is a promising path.

From Observation to Theory

2018 ◽  
pp. 154-181
Author(s):  
Alister E. McGrath
Keyword(s):  
Natural Sciences ◽  
Careful Consideration ◽  
Christian Theology ◽  
Potential Significance ◽  
Existence Of God ◽  
The World ◽  
Intellectual Journey

How do we move from observing the world to developing more complex and sophisticated ways of representing and understanding it? This chapter examines the intellectual journey from observing our world to representing it in theory, focussing on three distinct processes that are widely believed to be important in this process—deduction, induction, and abduction. Each of these rational strategies is used in theological or philosophical arguments relating to the existence of God. In each case, careful consideration is given to its application both in the natural sciences and in Christian theology. Particular attention is given to the American philosopher Charles S. Peirce’s use of abduction, and its potential significance for Christian theology.

Rational Explanation in Science and Religion

2018 ◽  
pp. 124-153
Author(s):  
Alister E. McGrath
Keyword(s):  
Science And Religion ◽  
Natural Sciences ◽  
Christian Theology ◽  
Good Theory ◽  
Existence Of God ◽  
Rational Explanation

This chapter considers what it means to ‘explain’ something in the natural sciences and Christian theology. A number of theories of explanation are considered, including ‘ontic’ and ‘epistemic’ approaches to explanation. Their respective merits and applications are examined. Particular attention is paid to ‘unitative explanation’, the idea that a good theory is able to enfold other theories, or enable things which were previously seen as unrelated to be considered as part of a greater coherent whole. The implications of these reflections for theological explanation are then considered, with the focus on one of Thomas Aquinas’s famous arguments for the existence of God—the ‘Second Way’.

Making a World, Mathematically

2017 ◽  
Author(s):  
Roi Wagner
Keyword(s):  
Nineteenth Century ◽  
Mathematical Practice ◽  
Natural Sciences ◽  
Applicability Of Mathematics ◽  
The World ◽  
Hermann Cohen

This chapter looks at mathematics not only as subject to constraints but also as feeding back into the reality that shapes it. To show how mathematics changes the reality in which it evolves and reforms the world where it lives, the chapter follows three nineteenth-century post-Kantian German thinkers: Johann G. Fichte, Friedrich W.J. Schelling, and Hermann Cohen. It also offers a solution to Mark Steiner's formulation of Eugene Wigner's problem of the “unreasonable” applicability of mathematics to the natural sciences (or at least a reduction of the problem to a more containable intra-mathematical setting). It lends credence to the book's description of mathematical practice as a negotiation of various constraints by means of rearticulated, superposed, and deferred interpretations in a contemplated and experienced reality.

CHRISTIAN ETHICS AND THE CONCEPT OF CREATION

2006 ◽  
Vol 71 (2) ◽  
pp. 132-144
Author(s):  
Pieter H. Stoker
Keyword(s):  
Physical Reality ◽  
Physical World ◽  
Natural Sciences ◽  
Christian Ethics ◽  
Atomic Scale ◽  
Human Thought ◽  
The Past ◽  
Scientific Approach ◽  
History Of ◽  
The Universe

The endeavour of science is to find unity in multitude, relatedness in diversity, continuity in discontinuity. By this way reality is simplified for scientific conception and description. With its reliance on observational data and logic, and with the scientific approach to understand the complexity, functionality, rationality and interrelationship of every aspect of reality, natural sciences do bring forward fascinating new insights on the concealed secrets in natural structures and processes. The crucial position of time in the laws of the universe followed from the work of Newton in the late seventeenth century. Newton gave time an abstract existence, independent from nature. Einstein restored time to its place in the heart of nature, as an integral part of the physical world. From the implications of Einstein’s time, scientists made one of the most important discoveries in the history of human thought: that time, and hence all of physical reality, must have had a definite origin in the past. Thus natural sciences have to accept the concept of origin. God formed man to glorify him as his earthly steward by giving him dominion over creation. Man is therefore responsible to God, also in his formation of science, by which a miraculous world of boundless diversity and interrelationship from the atomic scale to astronomical vastness is revealed. If we also take account of the transcendental revealed principle of creation, scientific thought becomes open, also in our ethical responsibility.

Mīmāṃsā

2018 ◽  
Author(s):  
John A. Taber
Keyword(s):  
Physical World ◽  
Way Of Life ◽  
Existence Of God ◽  
Indian Science ◽  
The World ◽  
Basic Orientation ◽  
The One ◽  
Immortality Of The Soul ◽  
Insight Into ◽  
The Way

The school of Mīmāṃsā or Pūrva Mīmāṃsā was one of the six systems of classical Hindu philosophy. It grew out of the Indian science of exegesis and was primarily concerned with defending the way of life defined by the ancient scripture of Hinduism, the Veda. Its most important exponents, Śabarasvāmin, Prabhākara and Kumārila, lived in the sixth and seventh centuries ad. It was realist and empiricist in orientation. Its central doctrine was that the Veda is the sole means of knowledge of dharma or righteousness, because it is eternal. All cognition, it held, is valid unless its cause is defective. The Veda being without any fallible author, human or divine, the cognitions to which it gives rise must be true. The Veda must be authorless because there is no recollection of an author or any other evidence of its having been composed; we only observe that it has been handed down from generation to generation. Mīmāṃsā thinkers also defended various metaphysical ideas implied by the Veda – in particular, the reality of the physical world and the immortality of the soul. However, they denied the existence of God as creator of the world and author of scripture. The eternality of the Veda implies the eternality of language in general. Words and the letters that constitute them are eternal and ubiquitous; it is only their particular manifestations, caused by articulations of the vocal organs, that are restricted to certain times and places. The meanings of words, being universals, are eternal as well. Finally, the relation between word and meaning is also eternal. Every word has an inherent capacity to indicate its meaning. Words could not be expressive of certain meanings as a result of artificial conventions. The basic orientation of Mīmāṃsā was pragmatic and anti-mystical. It believed that happiness and salvation result just from carrying out the prescriptions of the Veda, not from the practice of yoga or insight into the One. It criticized particularly sharply other scriptural traditions (Buddhism and Jainism) that claimed to have originated from omniscient preceptors.

Emilie du Châtelet

Philosophy ◽  
2020 ◽  
Author(s):  
Karen Detlefsen
Keyword(s):  
21St Century ◽  
18Th Century ◽  
Natural Philosophy ◽  
Physical World ◽  
Intellectual Life ◽  
Existence Of God ◽  
Mathematical Skills ◽  
The Bible ◽  
Foundations Of Physics ◽  
Heated Debate

Emilie Du Châtelet (b. 1706–d. 1749) was a French philosopher, author, and translator who worked primarily in natural philosophy, but also wrote on language, produced Biblical criticism, tackled questions surrounding virtue and happiness, and grappled with the nature of liberty given her understanding of the physical world and of God. She wrote and published, in her lifetime, on fire (having conducted a range of experiments on the topic at her family’s estate at Cirey), on natural philosophy more generally, and on the vis viva controversy. Much of her work was published posthumously, including work on optics, happiness, the Bible, language, and Newtonian philosophy. She was an avid translator, often developing her own original positions in her liberal changes made to texts in translation. This is especially true of her translation of Mandeville’s Fable of the Bees. Her translation of Newton’s Principia was the first translation into French of that work and remains the standard translation to this day. Having received training from many top mathematicians of her day, Du Châtelet’s own mathematical skills were notable, contributing to her facility in translating and discussing Newton’s work. She had a notable impact on European intellectual life during her lifetime, and in the form of several articles in the Encyclopédie, drawn often verbatim from her oeuvres. After falling largely into obscurity for the better part of two centuries, her thought has been revived across the globe, and 21st-century attention paid to this remarkable thinker has been especially robust. Her masterwork, The Foundations of Physics, addressed questions of method; metaphysics (for example, the nature of substance and body, and God’s existence and nature); and physics. She engaged especially with the works of Descartes, Leibniz, Wolff, and Newton, carving out original philosophical positions on a range of topics in natural philosophy. Her arguments for the nature and existence of God are also attuned to the contributions of Locke. In this text, as well as others, she engaged with Jean-Jacques Dortous de Mairan—then Secretary of the Académie Royale des Sciences—in a heated debate about vis viva, with Mairan taking the Cartesian position, and Du Châtelet arguing for the Leibnizian side. This extended exchange allowed Du Châtelet to engage with one of the most powerful men in science in mid-18th-century France, a significant feat given her exclusion from the Académie due to her gender. She collaborated or conversed with Voltaire, Francesco Algarotti, Pierre-Louis Moreau de Maupertuis, and Alexis-Claude Clairaut, among others, and her correspondents included Maupertuis, Algarotti, and Johann Bernoulli.

scholarly journals Gregory Palamas and our Knowledge of God

Studia Humana ◽  
2014 ◽  
Vol 3 (1) ◽  
pp. 3-12
Author(s):  
Richard Swinburne
Keyword(s):  
Physical World ◽  
Considerable Degree ◽  
Direct Access ◽  
Existence Of God ◽  
Knowledge Of God ◽  
Almost All

Abstract Although Gregory wrote very little about this. he acknowledged that natural reason can lead us from the orderliness of the physical world to the existence of God; in this, he followed the tradition of Athanasius and other Greek fathers. Unlike Aquinas, he did not seek to present the argument a; deductive: in fact his argument is inductive, and of die same kind as - we now realize - scientists and historians use when they argue from phenomena to then explanatory cause. Gregory wrote hardly anything about how one could obtain knowledge of the truths of the Christian revelation by arguments from non-question-beggining premises; but in his conversations with the Turks he showed that he believed that there are good arguments of this kind. Almost all of Gregory's writing about knowledge of God concerned how one could obtain this by direct access in prayer: this access, he held is open especially to monks, but to a considerable degree also to all Christians who follow the divine commandments.

scholarly journals Mixture and Transformation in Aristotle’s De generatione et corruptione

2018 ◽  
Vol 9 (1) ◽  
pp. 53-69
Author(s):  
Arman Zarifian
Keyword(s):  
Physical World ◽  
Natural Sciences ◽  
The Subject ◽  
Material Bodies ◽  
Small Parts ◽  
Substantial Change ◽  
Simple Combination

In his works on natural sciences, primarily in the Physics, Aristotle focuses on different forms of metabolē and distinguishes movement in general from substantial change. The On generation and corruption deals with the latter. When reading this treatise, one should pay particular attention to the concept of mixture. Apart from being the subject of a specific chapter (I 10), the problem of mixture permeates the whole work. But what exactly is mixture? Is it a simple combination of small parts? Can a compound of water and wine be called mixture? If so, is this mixture and nothing more? In the course of the discussion, it is argued that the Aristotelian idea of mixis does not correspond to the concept that is usually associated with it. Rather, it is shown that mixis is fundamental for comprehending the physical world and constitutes not only the term per quem the first elements of all material bodies originate, but also plays a fundamental role in all natural sciences, particularly, in biology.

Fictionalism in the philosophy of mathematics

2018 ◽  
Author(s):  
Mark Colyvan
Keyword(s):  
Philosophy Of Mathematics ◽  
Mathematical Discourse ◽  
Literary Fiction ◽  
Scientific Theories ◽  
Adequate Account ◽  
Mathematical Realism ◽  
Applicability Of Mathematics ◽  
Coming To Know ◽  
In Virtue Of ◽  
Error Theories

Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as ‘8+5=13’ and ‘∏ is irrational’, are to be interpreted at face value and, thus interpreted, are false. Fictionalists are typically driven to reject the truth of such mathematical statements because these statements imply the existence of mathematical entities, and according to fictionalists there are no such entities. Fictionalism is a nominalist (or antirealist) account of mathematics in that it denies the existence of a realm of abstract mathematical entities. It should be contrasted with mathematical realism (or Platonism) where mathematical statements are taken to be true, and moreover are taken to be truths about mathematical entities. Fictionalism should also be contrasted with other nominalist philosophical accounts of mathematics that propose a reinterpretation of mathematical statements, according to which the statements in question are true but no longer about mathematical entities. Fictionalism is thus an error theory of mathematical discourse: at face value mathematical discourse commits us to mathematical entities; and although we normally take many of the statements of this discourse to be true, in doing so we are in error (cf. error theories in ethics). Although fictionalism holds that mathematical statements implying the existence of mathematical entities are strictly speaking false, there is a sense in which these statements are true - they are true in the story of mathematics. The idea here is borrowed from literary fiction, where statements like ‘Bilbo Baggins is a hobbit’ is strictly speaking false (because there are no hobbits), but true in Tolkien’s fiction The Hobbit. Fictionalism about mathematics shares the virtue of ontological parsimony with other nominalist accounts of mathematics. It also lends itself to a very straightforward epistemology: there is nothing to know beyond the human-authored story of mathematics. And coming to know the various fictional claims requires nothing more than knowledge of the story in question. The most serious problem fictionalism faces is accounting for the applicability of mathematics. Mathematics, unlike Tolkien’s stories, is apparently indispensable to our best scientific theories and this, according to some, suggests that we ought to be realists about mathematical entities. It is fair to say that there are serious difficulties facing all extant philosophies of mathematics, and fictionalism is no exception. Despite its problems fictionalism remains a popular option in virtue of a number of attractive features. In particular, it endorses a uniform semantics across mathematical and nonmathematical discourse and it provides a neat answer to questions about attaining mathematical knowledge. The major challenge for fictionalism is to provide an adequate account of mathematics in applications.

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